The invention relates to fuel injection pumps for internal combustion engines having a housing, one pumping chamber and at least one reciprocating pump piston, arranged to open a discharge channel of the pumping chamber that is adapted to be blocked at starting rpm, and further with a pump which supplies fuel at an rpm-dependent pressure especially in the suction chamber of the injection pump. In a known fuel injection pump the blocking of the discharge channel at starting rpm occurs by means of an annular slide which is disposed around the pump piston and thus controls the injection quantity. In this manner there is a direct dependence of the shut-off of the starting quantity on the rpm and load-dependent adjusted position of the annular slide and of the fuel injection quantity associated with this position. For many internal combustion engines, however, it is desirable that an increased quantity of fuel continue to be injected during starting even after engine starting speeds are exceeded, certainly at least until the engine is running quite rapidly.